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Literature Cited
L. C. Lewis, “Quasiconformal mapping and Royden algebras in space,” Trans. Am. Math. Soc.,158, No. 2, 481–496 (1971).
S. K. Vodop'yanov and V. M. Gol'dshtein “Quasiconformal mappings and spaces of functions with first generalized derivatives,” Sib. Mat. Zh.,17, No. 3, 515–531 (1976).
Yu. G. Reshetnyak, “The concept of capacity in the theory of functions with generalized derivatives,” Sib. Mat. Zh.,10, No. 5, 1109–1138 (1969).
V. G. Maz'ya and V. P. Khavin, “Nonlinear potential theory,” Usp. Mat. Nauk,27, No. 6, 67–138 (1972).
P. I. Lizorkin, “Characteristics of the boundary values of functions in L rp (En) on hyperplanes,” Dokl. Akad. Nauk SSSR, 150, 984–986 (1963).
S. K. Vodop'yanov, V. M. Gol'dshtein, and Yu. G. REshetnyak, “On the geometric properties of functions with first generalized derivatives,” Usp. Mat. Nauk,34, No. 1, 17–66 (1979).
Yu. G. Reshetnyak, “On the boundary behavior of functions with generalized derivatives,” Sib. Mat. Zh.,13, No. 2, 411–419 (1972).
S. K. Vodop'yanov and V. M. Gol'dshtein, “A criterion for the removability of sets for the spaces L lp of quasiconformal and quasiisometric mappings,” Sib. Mat. Zh.,18, No. 1, 48–68 (1977).
F. W. Gehring, “Lipshitz mappings and the p-capacity of rings in n-space,” in: Advances in the Theory of Riemann Surfaces, Proc. Conf., Stony Brook, New York (1969), Princeton-New York Univ. Press (1971), pp. 175–193.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 3, pp. 55–61, May–June, 1984.
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Gol'dshtein, V.M., Romanov, A.S. Transformations that preserve Sobolev spaces. Sib Math J 25, 382–388 (1984). https://doi.org/10.1007/BF00968977
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DOI: https://doi.org/10.1007/BF00968977